fredag 28 februari 2014

Newton envisioning a trajectory of free fall by watching an apple fall and contemplating about a possible New View of gravitational motion without instant action at distance.

In the New View of Gravitational Motion the gravitational potential $\phi (x,t)$ is primordial with mass density $\rho (x,t)$ derived as $\rho (x,t) =\Delta\phi (x,t)$, formally by differentiation as instant local action in space with Euclidean coordinate $x$ and with $t$ a time coordinate.

In the Standard View instead the mass density $\rho (x,t)$ is primordial and the gravitational potential $\phi (x,t)$ is formally generated as solution to Poisson's equation $\Delta\phi (x,t)=\rho (x,t)$ as instant global action in space.

The basic mystery in the Standard View is the instant action at distance acknowledged by the inventor Newton himself:

That gravity should be innate, inherent and essential to matter, so that one body may act upon another at-a-distance, through a vacuum, without the mediation of anything else by and through which their action may be conveyed from one to another, is to me so great an absurdity that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it.

So far I have explained the phenomena by the force of gravity, but I have not yet ascertained the cause of gravity itself. ... and I do not arbitrarily invent hypotheses. (Newton. Letter to Richard Bentley 25 Feb. 1693)

There is no progress towards a resolution of the absurdity of instant action at distance. The New View offers a way to get around this basic difficulty instead of running head-on into it.

The New View presents gravitational motion by an evolution equation for the gravitational potential expressing mass conservation (with the dot indicating differentiation with respect to time):

$\Delta\dot\phi +\nabla\cdot (u\Delta\phi ) = 0$,

combined with an equation defining free fall trajectories $x(t)$ as the motion of immaterial pointwise particles according to Newton's 2nd law:

$\ddot x(t) +\nabla\phi (x(t),t) = 0$,

which define the immaterial velocity $u(x(t),t) =\dot x(t)$ in the evolution equation for $\phi$.

Motion under gravitation is thus according to the New View described by the following set of equations in terms of the gravitational potential $\phi (x,t)$ and immaterial free fall trajectories $x(t)$;

$\Delta\dot\phi +\nabla\cdot (u\Delta\phi ) = 0$,

$u(x(t),t)=\dot x(t)$,

$\ddot x(t) +\nabla\phi (x(t),t) = 0$,

where the mass density $\rho (x,t)$ does not appear, but is instead tied to $\phi (x,t)$ by the relation $\rho (x,t)=\Delta\phi (x,t)$ by differentiation as instant local action in space. Notice that the immaterial trajectories cover space even where $\Delta\phi (x,t)=0$ expressing absence of matter. The differential equations 1-3 are complemented by initial conditions $\phi (x,0)$ and $x(0)$ and $\dot x(0)$.

The New View would be the view of an observer who is blind to real matter, but can envision immaterial free fall trajectories $x(t)$ and instant local action. In the New View the gravitational potential changes and as result moves matter. Watching an apple fall is envisioning a free fall trajectory and corresponding change of gravitational potential.

The Standard View is natural to an observer who can envision real matter and instant action at distance, but is blind to immaterial free fall trajectories. In the Standard View matter moves and as a result changes the gravitational potential.

The New View and Standard View describe the same physics, for example the Earth moving around the Sun or a falling apple. The Standard View requires instant action at distance, which is unthinkable physics. The New View involves instant local action, which is thinkable physics.

attributing the energy $E=h\nu$ to a wave of frequency $\nu$, as a smallest quantum of energy of the frequency $\nu$. Planck used the quantum of energy $h\nu$ to save the scientific world from the ultra-violet catastrophe of classical electromagnetics with radiation energy scaling with $\nu^2$ without limit for increasing frequency $\nu$, using a statistical argument suggesting low probability of high frequency, thus effectively introducing a high-frequency cut-off in the radiation spectrum. Planck viewed his quantum as a mathematical trick without physical reality.

Then Einstein entered the game in 1905 with the article giving him the 1921 Nobel Prize in Physics presenting a formula expressing an energy balance for the photoelectric effect with electrons being ejected from a surface when exposed to light:

$ h\nu = E + P$

where $E$ is the energy of an ejected electron and $P$ the energy required to release the electron from the surface. With this formula, where $h\nu$ would represent a smallest quantum of light of frequency $\nu$, Einstein seemed to explain the basic properties of the photoelectric effect: No electrons are ejected unless $h\nu > P$ independent of light intensity and the number of ejected electrons scale with intensity. The value of $h$ was determined in 1916 by Millikan using Einstein's formula with the objective to falsify Einstein's concept of quantum of light.

Neither did the Nobel Committee buy Einstein's derivation of his formula based on light quanta, but with the appearance of quantum mechanics in 1925 Einstein's idea received momentum and with the name photon by Lewis in 1927 became a trademark of modern physics, although it was basically the same old corpuscular theory of light once suggested by Hobbes but quickly replaced by the wave theory of Huygens. In the Standard Model ruling fundamental physics of today the photon has as a respectable position as the elementary particle carrying the electromagnetic force. Light as a flow $\nu$ photons per unit time then correponds to an energy flux of $h\nu^2$, which we now compare with Planck's Law.

Let us in particular check out how Planck's constant enters into Planck's Law, which reads

We see that Planck's constant $h$ enters into Planck's law as a high-frequency cut-off for $\frac{\nu}{T} > \frac{10k}{h}$, which reflects the original role of $h$ given by Planck, with the dependence on $T$ reflecting Wien's displacement law.

Leibniz develops a solution of the mind-body problem arising from the dualism of Descartes as an analogy to the well known physical phenomenon of resonance between two pendula or tuning forks swinging in perfect harmony together:

Leibniz World is a world in such perfect harmony, and as such a Best of Worlds, with everything in resonance with everything else as an expression of Pre-established Perfect Harmony without cause-effect.

Another example is a coldblooded animal with temperature in perfect harmony with that of the environment, again by a resonance phenomenon as analyzed in Computational Black Body Radiation:

Leibniz World is a Classical World in stationary state of resonance with forces in equilibrium, to be compared with a Modern World in rapid change from non-equilibrium of forces.

In a Classical World in a stationary state of resonance, a distinction between cause and effect cannot be made because the directional aspect of time, with a cause necessarily appearing before an effect, is missing. An example is the Newton's law of gravitation $\rho =\Delta\phi$ between mass density $\rho$ and gravitational potential $\phi$, possibly without cause-effect or in any case not with $\rho$ the cause and $\phi$ the effect, as discussed at length in the present sequence of posts.

In a Modern World changing in time the cause-effect relation is of basic importance, in particular for anyone with ambitions to exercise control and there are many. In a Modern World with the physics of control becomes of paramount importance, and then the basic idea of modern physics of force carrying particles comes in handy:

If you want to control something far away, just send some force carrying particles, like rockets or drones and you will be able to complete your mission.

A hot body is sending heat energy carrying particles named photons to warm up a cold body.

Gravitational forces between bodies are established by exchange of force carrying particles named gravitons.

Electromagnetic forces are transmitted by force carrying particles named photons.

Strong and weak nuclear forces are transmitted by force carrying particles named gluons and W/Z-bosons.

While there are rockets and drones, the physical existence of particles like photons and gravitons may be more fiction than reality.

Ambitions of control may be huge, while reality of control is another thing. The cause-effect relation may not be want you would like it to be.

Below is a modern physics view of a world filled with force carrying particles:

Modernity is change and cause-effect action expressed as Will to Power by Nietzsche and in the dynamics of a capitalistic system, in contrast to a classical society in equilibrium. But sociology and politics is not physics, and so the modernity of modern physics may be illusion more than reality.

The revolution into modern physics the beginning of the 20th century (relativity and quantum mecahnics) came along with a revolution of technology (car, telephone, electricity, oil) combined with revolutions in politics, art, music, where old systems were overthrown with radical novelty of top priority. But physics is eternal and does not care about novelty, and so a lot of relevant classical physics (Newtonian mechanics and Maxwellian electromagnetics) was dumped in modern physics.

Modernity as motion was expressed in the avant-garde art movement of futurism:

måndag 24 februari 2014

A Galilean transformation gives the connection between the coordinates in one system at rest and another system translating with constant velocity with respect that at rest. Fundamental with a clear physical meaning and relevance.

Lorentz transformation with $x^\prime$-axis in red pointing into the $(x,t)$ first quadrant making it unphysical since different parts of an object extended in space get different time coordinates and thus does not exist as an object. For this reason, Einstein only speaks about points in space-time as events which excludes interactions of objects extended in space.

The coordinates in two space-time coordinate system $S$ and $S^\prime$ with coordinates $(x,t)$ and $(x^\prime ,t^\prime )$ moving with constant velocity $v$ with respect to each other is in classical (non-relativistic) mechanics connected by a Galilean transformation:

$x^\prime =x - vt$,

$t^\prime =t$,

In relativistic mechanics according to Einstein's special theory, the connection is instead postulated to be that of a Lorentz transformation:

In the Galilean case the time rate in $S$ and $S^\prime$ are the same, but in the Lorentz case it differs with a factor $\gamma$, so that with $S$ motionless the time in $S^\prime$ would seem to run slower, and the other way around.

The Lorentz transformation is by physicists regarded to reveal deep truths about physics, as a result of the fact that it leaves a wave equation in $(x,t)$ coordinates:

invariant under a Lorentz transformation, that is the wave equation looks precisely the same in $(x^\prime ,t^\prime )$ coordinates.

On the other hand, a Galilean transformation brings in a second order correction term in the velocity $v$ of the form:

$v^2 \frac{\partial^2u}{\partial x^2}$,

and therefore a Galilean transformation is not viewed to have the same dignity as the Lorentz transformation without such a correction. For human observations $v^2 < 10^{-10}$ (with the speed of light normalized to 1) the correction is miniscule and of no practical significance.

However, as strongly emphasized by Lorentz himself, the Lorentz transformation is not a transformation between physical coordinates. In particular the transformed time $t^\prime$ should not be viewed as real physical time.

This was not understood correctly by Einstein, who gave $t^\prime$, against the strong advice by Lorentz, a physical meaning and so the special theory of relativity was born based on the Lorentz transformation, which then (surprisingly against all odds) became a fundamental pillar of modern physics. Anything which is not Lorentz invariant is not modern physics!

And there we are today with the Lorentz transformation as a Holy Doctrine of Modern Physics of the same stature, and mysticism, as the Doctrine of the Holy Trinity of the Catholic Church. But a Lorentz transformation is just a very simple linear coordinate transformation and as such cannot reveal deep truths of physics, while the Holy Trinity may well represent a deep truth of religion.

Newtonian mechanics is Galilean invariant, but not Lorentz invariant, and so in Einstein's hands Newtonian mechanics had to be sacked, according to the Doctrine of Lorentz Transformation. Instead a wonderful magical world of space contraction and time dilation was born from the Doctrine, but of course inheriting the unphysical nature of the Lorentz transformation and thus only a world of illusions without the reality of Newtonian mechanics.

Curved space coordinate system in which free fall follows coordinate lines. Believing that this coordinate system shows us the true "fabric of curved space-time" is deeply mystical, yet supposed to be a foundation of modern physics.
In general relativity the distribution of matter/energy is supposed to determine the "fabric of space and time" and make more or less "curved" according to Einstein's equation (assuming the speed of light and gravitational constant normalized to unity)

$G_{\mu\nu}=8\pi T_{\mu\nu}$,

where $G_{\mu\nu}$ is Einstein's tensor measuring curvature and $T_{\mu\nu}$ is a stress-energy tensor. The folklore explanation in the words of John Wheeler reads as follows:

In the basic case of flat Minkowski space-time and infinite speed of light (standard Euclidean space with coordinate $x$ and separate time coordinate $t$), Einstein's equations reduce to

Newton's equations

$\Delta\phi =\rho$, (Newton's law of gravitation)

$\ddot x(t) + \nabla\phi (x(t),t)=0$, (Newton's 2nd law)

where $\rho (x,t)$ is mass density, $\phi (x,t)$ is gravitational potential and $x(t)$ denotes the trajectory of a mass particle moving subject to gravitational forces given as $-\nabla\phi (x,t)$. As a Wheeler paraphrase, Newton's equations could be expressed:

Matter determines the gravitational potential. The gradient of the gravitational potential determines how matter moves.

Einstein's supposedly great idea was to reduce all motion to free fall in a space-time coordinate system where the equations of motion take the form $\ddot x(t)=0$ as if no gravitational forces were present.

Einstein thus replaces the gravitational potential by space-time curvature, which makes things more complicated, and then balances by using a trivial form of Newton's 2nd law.

The question is if there is a net gain or loss by this shift? I would vote for Newton's formulation because both Newton's laws are easy to grasp. On the other hand, Einstein's concept of "curved space-time" supposedly being realized in some "fabric of space-time" makes things much more difficult to grasp at the small gain of having only to deal with Newton's 2nd law in trivial form, thus with a net loss.

Einstein's was hooked to the idea of choosing a coordinate system in which the equations of motion reduce to the trivial form for free fall, as if the essence of physics was hidden in a coordinate system.

But real physics cannot rely on the choice of coordinate system. In principle any coordinate system can be used and a coordinate system does not need any "fabric" to be erected as it is immaterial.

Believing that there are certain coordinate systems with higher scientific value than others, may lead to seek to identify such royal coordinate systems through some form of material existence expressed as "fabric of space-time". But that is deeply mystical and as such can only be an illusion.

Newtonian gravitation can be combined with Maxwell's equations for electromagnetics and Schrödinger's equations for quantum mechanics into a Unified Field Theory. Einstein struggled for 40 years to combine Einstein's equations with Maxwell's and Schrödinger's equations without any success, and nobody else got further.

The effective way out of this dilemma, which has paralyzed physicists for 100 years, may well be to replace Einstein's equations by Newton's equations at no loss of anything of real value to physics.

Gravitational potential generating mass at the tip of the potential well.

Viewing physics as a form of analog computation based on computational exchange of local information, suggests that instant action at distance is unphysical, because a large number of local computations would be required to transfer information globally, which would require time.

Newton's law of gravitation can be expressed through the relation $\Delta\phi (x,t) =\rho (x,t)$, where $\phi (x,t)$ is gravitational potential and $\rho (x,t)$ mass density with $x$ a Euclidean space coordinate. The potential $\phi $ may be computed by explicit time stepping to stationary state, each step exchanging local information only, of the parabolic evolution equation (heat equation)

which would require time and thus cannot be accomplished instantly. Here a dot signifies differentiation with respect to time $t$.

We conclude that in the relation $\Delta\phi =\rho$ connecting $\phi$ and $\rho$, we cannot view $\rho$ as input or cause and $\phi$ as output or effect, but rather the other way around with the potential $\phi$ as primordial input/cause and $\rho$ as the output/effect. With this view $\rho (x,t)=\Delta\phi (x,t)$ is produced locally by the Laplacian differential operator $\Delta$ acting locally in space on the potential $\phi (x,t)$, thus without action at distance and thus in principle allowing instant action.

We may compare with Faraday's law of induction in electromagnetics:

$J = -\dot E + \nabla\times B$,

where $J(x,t)$ is electrical current density, $E$ is electrical field and $B$ magnetic field, which can also be expressed by the wave equation

$-\dot J =\ddot E -\Delta E \equiv\square E$,

with a common notation. Here we see the current $J$ being generated by the electrical field $E$ by differentiation acting locally in space and time and we thus face a concrete physical example of a field by generating a flow of charge or current locally by differentiation. By analogy we may envision the gravitational field $\phi$ generating mass $\rho =\Delta\phi$ locally by differentiation.

We thus have the following two relations with the fields $\phi$ and $E$ acting as input and the output $\rho$ and $\dot J$ being produced locally by differentiation:

$\rho = \Delta\phi $,

$\dot J =- \square E$ or $J = -\dot E + \nabla\times B$.

Here 2 expresses the familiar physics of induction, while 1 expresses unfamiliar generation of mass by gravitational potential. The question if we can learn to become as familiar with 1 as we already are with 2? Von Neumann reflected:

In mathematics you don't understand things. You just get used to them.

Maybe it is the same with physics, and then it seems better to get used to constructive real physics which can be simulated by digital computation, than with illusionary physics, which can only be simulated by illusions of thinking without connection to the realities of physics. Such an illusion is instant action at distance as in the conventional view of gravitation with matter generating gravitational potential and force.

Motion of a magnet generates a current from changing electrical field.

Maxwell's equations can be formulated (assuming unit speed of light):

$\dot B + \nabla\times E = 0$

$\dot E - \nabla\times B = - J$

$\dot\rho + \nabla\cdot J =0$,

where $E(x,t)$ is the electric field, $B(x,t)$ the magnetic field, $\rho (x,t)$ charge density and $J$ electric currentdensity, given as $J=\rho v$ with $v$ charge velocity, or by a constitutive law such as Ohm's law

$J =\sigma (E + v\times B)$,

where $\sigma$ is a conductivity and $v$ the velocity of the conducting medium. The dot indicates differentiation with respect to time $t$, while $x$ is a Euclidean space coordinate.

Differentiating 2 with respect to time and applying $\nabla\times$ to 1, gives the following wave equation for the electric field:

There are two possible ways of viewing Maxwell's equations in terms of input and output:

(I) Input: charge and current, Output: electric and magnetic fields,

(II) Input: electric and magnetic fields, Output: charge and current.

Here (I) corresponds to solving wave equations with $\rho$ and $J$ given input producing as output $E$ and $B$ as action at distance with a time delay because of finite speed of light, or the static Poisson equation with potential $\phi (x)$ as output by action at distance from $\rho (x)$ without time delay aspect.

Further $(II)$ correspond to instantaneous local action by electric/magnetic fields to produce $\dot J(x.t)$ or $\rho (x)$. This is the physical process of electromagnetic induction.

In electromagnetics, both cases appear, with an example of (II) given in the above picture.

Maxwell's equations are Galilean invariant modulo a second order factor $\frac{v^2}{c^2}$ with $c$ the speed of light, see Many Minds Relativity Chapter 17. The speed difference between human observers can differ by at most a few $km/s$, while $c\approx 300.000\, km/s$, and thus the factor is smaller than $10^{-10}$. Maxwell's equations can thus in practice be viewed by human observers to be Galilean invariant, which makes Lorentz invariance irrelevant.

In the New View of Motion under Gravitation we consider in the basic relation $\Delta\phi =\rho$, the gravitational potential $\phi (x,t)$ to be primordial and the mass density $\rho (x,t)$ to be derived from
$\phi (x,t)$ by instantaneous local action in space of the Laplace differential operator.

In the standard view instead the mass density $\rho (x,t)$ is viewed to be primordial and the potential
$\phi (x,t)$ is viewed to be derived as the solution to the equation $\Delta\phi =\rho$ by instantaneous action at distance in a solution process which can be described as global integration:

Why then is $\rho$ chosen to be primal (input) and $\phi$ secondary (output) in the standard view? The answer appears to be twofold:

Matter is visible to the human eye, while gravitational potential and forces are invisible.

Matter distribution can easily be imagined by the human mind as input, while corresponding gravitational potential and forces are more difficult to grasp (output).

A human mind may thus be led to the standard view by reasons which are superficial from physics point of view. In particular, if we consider physics to be some form of computational process, we expect that intantaneous action at distance as instantaneous solution of the differential equations $\Delta\phi =\rho$, cannot be realized as a physical process. The standard view would then seem to be unphysical, and rather reflect how human minds see things than how things in fact are.

fredag 21 februari 2014

Imagine that each atom of the Earth is communicating with each atom of the Sun by exchanging force carrying particles named gravitons through which a gravitational force is established between each such pair of atoms (neglecting internal gravitation for simplicity).

The number of atoms in the Earth is estimated to be around $10^{50}$ and that in the Sun around $10^{57}$, which gives a number of pairs much larger than a $googol = 10^{100}$, while the total number of atoms in the Universe may be of order $10^{80}$.

To store the total set of gravitational forces between the Earth and the Sun, thus would require a hard disk much heavier than the Universe, and there would be no place for the gravitational force between the Earth and the Moon, to name one example.

Do you now start to feel that there is something strange about the standard model of gravitation, which is precisely the one described above?

Do you now start to feel that the very idea of each atom of the Universe making its presence felt to all other atoms of the Universe by creating a gravitational field extending over the entire Universe, is very strange or more precisely describes a complete impossibility?

Do you now start to feel that the Millennium Run with $10^{10}$ particles interacting by gravitation requires way to much computational work to represent physics?

Do you now start to think that maybe, maybe, it is the other way around; that is that the gravitational potential $\phi$ and gravitational field $\nabla\phi$ is primordial and that matter with density $\rho$ is generated locally formally by differentiation as $\rho =\Delta\phi$?

torsdag 20 februari 2014

Is Hermes as boson as carrier of force between fermions Greek mythology rather than physics?

The Standard Model identifies two main types of elementary particles: fermions as carriers of charge and mass such as the electron and proton, and bosons as carriers of force such as the photon supposedlycarrying the electromagnetic force and carriers of the weak and strong nuclear force.

The Standard model thus includes the electromagnetic, weak and strong forces, but the 4th fundamental force of gravitation is excluded, which is viewed to be a main defect of the Standard Model defying all attempts of correction.

The hypothetical carrier of the gravitational force is the graviton, but there is no experimental evidence of the existence of such a particle.

From these facts, it is natural to question the fundamental idea of the Standard Model that there are certain carriers of forces in the form of boson particles carrying forces over distance between fermions: If there is no particle carrying the gravitational force from the Sun to the Earth, why must there be a particle named photon carrying electromagnetic forces from mobile telephone mast to the mobile phone in our hand, like a Hermes of electromagnetics? A particle without mass and charge which has not been identified experimentally.

In the New View we turn the perspective around and view the boson force field with everywhere presence in space as primordial from which the fermion field is locally generated and acted upon without any need of carrying force over distance. This opens to a reduction of the number of elementary particles by eliminating particles serving the purpose of carrying forces around.

In the New View the force field is everywhere present and is not carried around. In the New View the gravitational field is everywhere, from which matter is locally generated thus eliminating the need of instantaneously carrying force over distance.

Sound is a wave phenomenon as local variation of a pressure field in air. Sound is not a corpuscular flow of sound particles named phonons flying from source to ear.

Light is a wave phenomenon as local variation of an electromagnetic field in a vacuum. Light is not a corpuscular flow of light particles named photons flying from source to eye.

Modern physics dominated by elementary particle physics based on the Standard Model is based the idea of particles as pointlike (or stringlike) carriers of charge and mass (fermions) and forces (bosons).
The Standard Model today consists of a wild zoo of 61 particles and physicists have since 50 years desperately been seeking alternative models with particles replaced by one-dimensional strings or two-dimensional branes, however without much success.

A pointlike elementary particle is supposed to have a dual wave character as a distributed field in what is referred to as wave-particle duality with the idea that both characters can show up in different situations, like Dr Jekyll-Mr Hyde or schizofrenia syndrom.

The carrier of the electromagnetic force is an elementary particle named photon, by which the propagation of light is described as a stream of photon particles, much like the corpuscular theory of light proposed by Thomas Hobbes in 1643 and adopted by Newton. The corpuscular theory of light was replaced by Huygen's wave theory of light once Newton had faded away and reached a completion with Maxwell's equations (1862) describing virtually all of electromagnetics including light by set of wave equations for electric and magnetics fields, an unprecedented triumph of mathematical physics.

With the formidable success of Maxwell's equations describing light as wave, one would imagine that any corpuscular theory of light could safely be put into the dustbin of scientific garbage, but then Einstein entered the game in 1905, stimulated by the energy quanta suggested by Planck in 1900 to avoid the ultraviolet catastrophe of blackbody radiation, with an idea of light quanta as a corpuscular particle theory of light picked up from the dustbin in an attempt to "heuristically" explain the photoelectric effect.

Einstein's particle idea then combined with the new atom physics in the form of quantum mechanics based on Schrödinger's wave equation, connected by a trick of wave-particle duality invented by Bohr.

Since schizofrenia is a serious syndrome, one may ask what makes modern physicists cling to a primitive particle theory of light as a stream of photons, when there is an educated wave theory in the form of Maxwell's equations?

Why not get rid of the primitivism of a corpuscular theory of light once and for all? Or is a corpuscular theory of light only a harmless heuristic way of thinking, which we can use if we want to explain things to kids?

No, it is not harmless and in fact the opposite because it creates artificial mysteries draining human and material resources with questions without answers like:

What is a photon particle?

How do photon particles travel?

What is the speed of a photon particle?

How do photon particles interact with matter?

To understand how silly these questions occupying physicists minds, let us compare light with sound:

We know that sound is a wave phenomenon of pressure variations supported by vibrating air molecules.

We know that sound is not a stream of sound particles as phonons from source to ear.

We know that transfer of sound from source to eardrum is a resonance phenomenon between two resonators (vibrating membrane of loud speaker and eardrum) connected by a medium (air) supporting pressure variations transferring forces from membrane to eardrum.

The analog for light is developed as Computational Blackbody Radiation explaining that blackbody radiation is a resonance phenomenon of electromagnetic waves with a high-frequency cut-off avoiding the ultra-violet catastrophe by finite precision computation.

In short, there is as little reason to speak about photons as light particles as there is to speak about phonons as sound particles.

It is true that a simple mathematical model of sound propagation can be formulated as a particle model with sound particles moving along straight lines combined with simple reflection laws:

But this is only a simple mathematics model and does not describe the real physics of propagation of sound as a wave phenomenon. Neither does a particle model for light have anything to do with the real physics of light as wave.

The term elementary particle is thus misleading and should better be replaced by something like elementary wave. Hopefully the zoo of elementary particles can then be reduced to a smaller number of elementary waves. This the basic idea of string theory, which however is set to the excessively small size of Planck's quanta $\sim 10^{-34}$ beyond any physics rationale.

Quantum mechanics is a wave theory for atomic dimensions in which particles serve no purpose.

In the previous post we considered a system of two distant resonators E and R connected by electromagnetic waves in a vacuum between the resonators, which can take the following form

E = radio mast - vacuum - R = radio receiver

E = mobile phone mast - vacuum - R = mobile phone

E = radio star - vacuum - R = radio telescope

E = visible star - vaccum - R = telescope/eye.

The velocity of the E-vacuum-R system is here irrelevant as the system acts like one unity with E and R being connected by standing waves carried by an immaterial vacuum, which can be assumed to "move along with" E and R.

The Michelson-Morely experiment was set up to detect possible motion of the Earth through an "ether medium" carrying electromagnetic waves, by comparing the travel time of light signals in two perpendicular directions using a system of mirrors:

But no motion could be detected as if the "ether medium" was "dragged along" by the Earth. This was viewed as a contradiction to classical electromagnetics described by Maxwell's equations. To handle the illusion of contradiction, relativity theory was developed seeking to explain the Michelson-Morely null result by entirely new phenomena of length contraction and time dilation, which sent modern physics into a nightmare of mysteries.

However, it is possible to explain the Michelson-Morley null result without resort to mysteries of relativity: If we consider each pair of mirrors as a rigid system connected by standing electromagnetic waves in a vaccuum, then the orientation and velocity of the system will not affect the inner working of the system. The system acts like a clock ticking at the same rate independent of orientation and velocity.

The key is that electromagnetic waves are carried by a vacuum which by its immaterial nature can be viewed to move along with the pair of mirrors. The immaterial nature makes it possible to envision many different vacuui. We cannot eat the same piece of food, but we can share the same immaterial ideas with any number of people.

This is developed further in Many-Minds Relativity based on the principle that each observer is fixed to the origin of a Euclidean coordinate and relies on Maxwell's equations in this coordinate as a representation of the vacuum carrying electromagnetic waves. Different observers moving with respect to each other thereby use different coordinate systems or vacuui. Different observers will then have the same experiences inside their respective systems as a reflection of the Michelson-Morley null result. Different observers will be able fully agree about certain observations such as Michelson-Morley and the speed of light, but not fully about all observations. Full coordination is not possible but nor necessary.

Einstein's special relativity seeks to establish full coordination by a dicate, but as any dictate against natural order, it is destructive.

Note that the resonators communicating by electromagnetic waves in a vaccum, connects to the New View of Motion under Gravitation without Classical Mysteries, where large scale material motion is an illusion created by real small scale circular wave motion. Energy is thus transferred from one resonator to the other by transversal electromagnetic wave motion in a vaccum, but there is no stream of "particles as packets of energy" through the vacuum connecting the resonators.

tisdag 18 februari 2014

Computational Blackbody Radiation describes radiative energy transfer as a resonance phenomenon between resonators connected by standing electromagnetic waves in a vacuum between the resonators. The acoustic analog is depicted above: Energy is transferred from one tuning fork to another by standing acoustic waves as pressure variations in still air.

In this model the finite speed of electromagnetic (or acoustic) waves only influences the energy transfer in a start up phase, while in a stationary state of standing waves the energy transfer can be viewed to be instantaneous without time delay, or to be without time aspect. The transfer of energy is one-way from hot (high frequency) to cold (low frequency).

In this view there is no need to introduce particles named photons carrying energy packets at finite speed back and forth between the resonators, as if the resonators were connected by a two-way highway with trucks transporting energy in both directions. There is no experimental evidence of the existence of such a two-way stream of light quanta. Einstein introduced light quanta in his annus mirablis 1905, but changed mind before passing away:

All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. (Albert Einstein, 1954)

The lights we see in the sky thus result from resonance by standing electromagnetic waves in the vacuum between our eyes and a distant star, and not by light particles having traveled for billions of years before hitting the retina of an eye. Energy is transferred from one tuning fork to the other by acoustic standing waves but there are no phonon particles carrying the energy by flying like a swarm of wasps between the forks.

The idea of a photon as an elementary particle acting as force carrier of the electromagnetic force, is a basic element of the standard model. No wonder that physicists are not happy with this model. The photon as carrier of the electromagnetic force like the graviton as carrier of the gravitational force, is probably Einstein's biggest mistake, far bigger than the cosmological fudge constant in Einstein's equations, and a return to the primitive corpuscular theory of light of Thomas Hobbes (1644), which was superseeded by Huygen's wave theory (1678), once Newton was dead, but then surprisingly popped up again in Einstein's 1905 article on the photoelectric effect.

In New View of Motion under Gravitation I suggest to view gravitational potential $\phi (x,t)$ as primordial and matter density $\rho (x,t)$ generated by $\phi$ by action of the Laplacian: $\rho (x,t) =\Delta\phi (x,t)$ which is local space and time, with $x$ a Euclidean space coordinate and $t$ time.

With this view there is no action at distance, which is the main unresolved mystery of Newton's mechanics with matter density $\rho$ primordial and gravitational potential $\phi$ as the solution of the differential equation $\Delta\phi =\rho$. Istant action at distance has never been explained.

Einstein's theory of relativity is viewed to be the highest achievement of human mind and imagination all times, but relativity theory is paradoxically based on a dictate to eliminate relativity by asking everybody to adopt a common view.

söndag 16 februari 2014

Einstein in the middle forcing all physicists at the Solvay conference 1927 to agree on a common universal standard of using the Lorentz transformation of special relativity. Everybody but Schrödinger above Einstein and Lorentz to the left agreed. Today you have to follow the Lorentz transformation standard if you aspire to get an academic job as physicist.

There are two main approaches to both philosophy, mathematics and physics (and other areas):

Constructivism - intuitionism - realism:

existence of real world independent of human hand and mind (stars, dinosaurs)

existence of real world constructed by human hand and mind (cars, computers)

existence of image of real world created by human hand and mind (math models, computer programs).

Formalism: idealism:

existence of sign - image created by human hand and mind (math models)

relation between sign - image and (real) world magical.

Einstein was an extreme formalist with an obsession for coordinate systems as formal systems for keeping track of points in space and time used by humans. There are many possible coordinate systems, which are all relative to each other and thus creates a mess of different views like the mess created by different religions or different political opinions.

Being an extreme formalist, Einstein developed both the special and general theory of relativity in a mission to bring order into the mess of relative coordinate systems by forming a universal standard forcing all observers using different coordinate systems to agree. The Lorentz transformation as foundation of the special theory, is thus a dictate to be followed when making observations using different inertial coordinate systems. Many Worlds - One Observer.

Newton's equations take the same form in all inertial systems connected by Galilean coordinate transformations. Maxwell's equations take the same form in all inertial coordinate systems connected by Lorentz transformations, but not by Galilean transformations. Einstein dictated that Maxwell's equations under Lorentz transformations should be the universal norm, and thereby declared Newton's laws as being outside the law of physics, while begging: Newton, forgive me!

Einstein's relativity theory dictates a universal standard of form, like forming a universal religion forcing everybody to formally confess to the same god, or all people in Europe to formally support the idea of the European Union (to pay tax), or use a gold standard for money, and thus paradoxically contradicts relativity.

For a constructivist, Einstein's dictated unification program would serve no purpose. Different people would be allowed to construct different images and have different gods and only a minimal coordination based on practical needs, would be called for, like a system of different floating currencies. The real World would be One, but there would be many different views depending on observer position. One World - Many Observers.

In this sense a constructivist is a true relativist, or democrat, while Einstein's relativity theory would rather reflect the opposite of absolutism (Ein Volk, ein Reich, ein Fuhrer). This aspect is developed in more detail in Many-Minds Relativity.

For a constructivist, the choice of coordinate system is a matter of convenience and does not hide any secrets of physics. For a formalist like Einstein, coordination of observations in different coordinate systems is of paramount importance with the goal of defining a universal standard, and the physisc is secondary if not nil.

The New View starts from gravitational potential and gravitational force as primordial and ends with matter by action local in space and motion as reality. Newton's 2nd law and the Equivalence principle are consequences of the New View and not ad hoc assumptions. The coordinate system is Euclidean without rotation since centrifugal forces are missing in 3, and with origin and translation at constant velocity free to choose. One such system is determined by the fixed stars, assuming no rotation of the visible Universe. Notice that a free fall trajectory $x(t)$ is immaterial and thus exists as solution to $\ddot x(t)=-\nabla\phi (x(t),t)$ also in vacuum where $\Delta\phi (x(t),t)=0$. The evolution equation for $\phi$ then express that matter moves along immaterial free fall trajectories. No medium for propagation of gravitational forces is required, because all action is local and trajectories are immaterial.
Free fall trajectories could be used to locally define curved coordinate systems, but reason to do so lacking.

General Relativity starts from matter creating curved space-time by action at distance gearing motion and ends with gravitational force as illusion. Einstein was led to General Relativity from the idea of extending Special Relativity with zero gravitation to the case non-zero gravitation by changing the coordinate system to give the illusion of zero gravitation. The Equivalence principle as ad hoc assumption serves to identify gravitational force with inertial force. Einstein based his physics on thought experiments with people being stuck in elevators in free fall. Einstein put the emphasis on the choice of coordinate system, as if real physics could depend on the coordinates chosen to describe physics.

Einstein thus developed a gravitational theory based on an idea that gravitation is illusion. No wonder if General Relativity is also only illusion and not physics.

Recall that Einstein fell in love with the idea of gravitational force as illusion, viewing it as the happiest thought of my life:

The gravitational field has only a relative existence... Because for an observer freely falling from the roof of a house -at least in his immediate surroundings - there exists no gravitational field.

Einstein's example shows the consequences of falling in love too much with an idea, in particular with an idea that serves your preconceived agenda.

Recall that modern theoretical physics is paralyzed by the incompatibility of general relativity with quantum mechanics, but physicists thoroughly trained to confess to the dogma of general relativity are unable to get out of the dead-lock. And so the happiest thought of Einstein's life has brought death to physics, in accordance with the logic of tragedy.

We now continue New View of Motion under Gravitation without Classical Mysteries with a study of the Equivalence Principle (EP) stating that inertial mass is equal to gravitational (heavy) mass, or in other words, that all matter independent of mass and composition reacts the same way to gravitation. EP was identified by Galileo and by Newton made into a corner stone of his theory of gravitation.

The question is if EP is a deep mystery or a necessity which can be understood? Why does a stone and a feather fall the same way when dropped from the Tower of Pisa (assuming no air resistance)? Is it mystery or not?

We recall our Newtonian model of matter subject to gravitation expressed by the equations (to be satisfied for all $x$ and positive time $t$):

where $\phi$ is a gravitational potential $\phi (x,t)$ depending on a Euclidean space coordinate $x$ and time $t$, and $\rho (x,t)$ is matter density and $x(t)$ denotes a trajectory with acceleration $\ddot x(t)$ and velocity $\dot x(t)=u(x(t),t)$ specified by initial conditions $x(0)$ and $\ddot x(0)$, with the dot denoting differentiation with respect to time.

We thus consider the gravitational potential $\phi$ as the primordial object and the matter density $\rho (x,t)$ as a derived physical quantity given by Newton's law of gravitation: $\rho (x,t) =\Delta\phi (x,t)$.

We consider trajectories $x(t)$ as mathematical constructs given by Newton's 2nd law in its mathematical form: $\ddot x(t)= -\nabla\phi (x(t),t)$. Newton's 2nd law in math from states a connection between motion $\ddot x(t)$ and the gradient of the gravitational potential $\nabla\phi (x,t)$, which can be viewed to reflect a balance between two types of energy:

KE(t) = $\frac{\vert\dot x(t)\vert^2}{2}$ (kinetic energy)

GE(t) = $\phi (x(t),t)$, (gravitational energy):

with

$\frac{d}{dt}(KE + GE)=0$.

We view $\rho (x,t) =\Delta\phi (x,t)$ as expressing local "creation of matter" with density $\rho (x,t)$ by "action" of the Laplacian differential operator $\Delta$ operating on the gravitational potential $\phi (x,t)$ locally in space and time. We note that the "creation of matter" does not depend on the nature or composition of matter, and we can thus view the created matter to be a form of primordial matter with only quality being density $\rho$ from which all matter with different nature and composition is formed.

We can then view Newton's 2nd law in physics form to express EP in the form:

Material motion under gravitation is independent of matter nature, composition and density.

We sum up:

EP is a consequence of Newton's 2nd law.

Newton's 2nd law serves to maintain a balance between kinetic energy depending on motion and gravitational energy depending on position.

The essence given by the Creator is thus a Universe with a dynamics in time based on a balance between two forms of energy, kinetic energy of motion and gravitational energy of position, maintained by Newton's 2nd law. In this Universe, EP is valid as a consequence of Newton's 2nd law.

Defining non-gravitational forces $F(x(t),t)$ by Newton's law in the form

Einstein's general theory of relativity is supposedly based on EP. If now EP is a consequence of Newton's 2nd law, we are led to the conclusion that Einstein's mechanics is no different from Newton's.

Comparison with Standard Newtonian Mechanics

If we now accept that EP is a consequence of Newton's 2nd law, it is natural to ask in what sense the New View may be more illuminating than the standard view?

In standard Newtonian mechanics, matter with density $\rho (x,t)$ is primordial with the gravitational potential $\phi$ being generated from $\rho$ as a solution of $\Delta\phi =\rho$ (requiring instant action at distance). The gravitational force acting on a lump of matter of density $\rho$ will then be given by $\rho\nabla\phi$ and EP will then, as above, be equivalent to Newton's law in the form $\rho\ddot x + \rho\nabla\phi=0$.

In this case matter of density $\rho$ appears in three forms: (i) as generator of gravitation in $\Delta\phi =\rho$, (ii) as gravitational mass in $\rho\nabla\phi$ and (iii) as inertial mass in $\rho\ddot x$, all supposed to be the same, which may be viewed as coincidence or as a mystery.

In the New View, $\rho =\Delta\phi$ appears in only one form as a product of $\phi$ combined with Newton's 2nd law in math form expressing a balance of kinetic and potential energies, and the equivalence of this form of mass with gravitational and inertial mass is simply a matter of definition and thus no mystery.

The New View thus opens to understanding that EP is rather a matter of definition, which is true by the construction of language, than a statement about physics, which may be true or false. In particular, it points to obvious difficulty of avoiding circular reasoning when seeking to test EP experimentally.

The third is … that the flying arrow is at rest, which result follows from the assumption that time is composed of moments … . he says that if everything when it occupies an equal space is at rest, and if that which is in locomotion is always in a now, the flying arrow is therefore motionless. (Aristotle Physics, 239b.30)

Zeno abolishes motion, saying “What is in motion moves neither in the place it is nor in one in which it is not”. (Diogenes Laertius Lives of Famous Philosophers, ix.72)

This argument against motion explicitly turns on a particular kind of assumption of plurality: that time is composed of moments (or ‘nows’) and nothing else. Consider an arrow, apparently in motion, at any instant. First, Zeno assumes that it travels no distance during that moment—‘it occupies an equal space’ for the whole instant. But the entire period of its motion contains only instants, all of which contain an arrow at rest, and so, Zeno concludes, the arrow cannot be moving.

Zeno was so clever in formulating his arrow paradox that it has resisted convincing resolution into our days. The commonly accepted "resolution" is the "at-at" theory put forward by Bertrand Russell, which simply says that the motion of an arrow appearing at different positions at different times can be described by a continuous function $f(t)$ where $f(t)$ is the position at time $t$. With a non-constant continuous function $f(t)$ of the real variable $t$, the arrow is thus changing position with increasing time and thus is moving. Russell writes in The Principles of Mathematics in the chapter on motion

Motion consists merely in the occupation of different places at different times, subject to continuity as explained in Part V. There is no transition from place to place, no consecutive moment or consecutive position, no such thing as velocity except in the sense of a real number which is the limit of a certain set of quotients. The rejection of velocity and acceleration as physical facts (i.e. as properties belonging at each instant to a moving point, and not merely real numbers expressing limits of certain ratios) involves, as we shall see, some difficulties in the statement of the laws of motion; but the reform introduced by Weierstrass in the infinitesimal calculus has rendered this rejection imperative.

According to the “at-at” theory, it is fallacious to conclude from the fact that the arrow does not travel any distance in an instant that it is at rest. Motion has nothing at all to do with what happens during instants; it has instead to do with what happens between instants. In short, motion is merely being in different locations at different times, and that is that. If an object has the same location at the instants immediately neighboring, then we say it is at rest; otherwise it is in motion. Therefore, since the arrow in flight has different positions at different instants, it is surely moving.

The “at-at” theory is a static theory of motion. In Henri Bergson’s cynical words, “movement is composed of immobilities.” (Bergson 1911, p.308) Continuous motion is simply the occupation, by an object, of a continuous series of places at a continuous series of times. There are no states of motion at an instant, and no instantaneous properties indicate that an object is moving or not.

We understand that the "at-at" theory is no theory, just a tautological play with words: To say that an arrow is moving because its position is changing with time is simply a truism or tautology and thus is empty of physical content. To disguise the emptiness, a reference is often made to Calculus and the definition of a continuous function through the concept of limit, but the physics is still lacking. Another form of hand-waving is to say the motion of an arrow is explained by the theory of relativity.

The net result is that Zeno's arrow paradox still after 2500 year lacks a real physical resolution. An attempt to such resolution was made in the previous post.